Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

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        <div xml:id="echoid-div87" type="section" level="1" n="72">
          <pb o="18" file="527.01.018" n="18" rhead="*I* L*IBER* S*TATICÆ*"/>
        </div>
        <div xml:id="echoid-div88" type="section" level="1" n="73">
          <head xml:id="echoid-head82" xml:space="preserve">PRAGMATIA.</head>
          <p>
            <s xml:id="echoid-s464" xml:space="preserve">Quandoquidem TI columnę diameter pendula eſt, Q B autĕ ponderis Y,
              <lb/>
            T Q jugum erit, ejusq́ue radius brevior X Q, X T vero longior. </s>
            <s xml:id="echoid-s465" xml:space="preserve">Inquiren-
              <lb/>
            dum igitur quæ ſit ratio X Q radii ad radium X T: </s>
            <s xml:id="echoid-s466" xml:space="preserve">eſto ex hypotheſi 1 ad 2.
              <lb/>
            </s>
            <s xml:id="echoid-s467" xml:space="preserve">Dico igitur ut X Q 1 ad X T 2: </s>
            <s xml:id="echoid-s468" xml:space="preserve">ita columna 6 ℔ ad quem? </s>
            <s xml:id="echoid-s469" xml:space="preserve">pro Y conclu-
              <lb/>
            ditur 12 ℔. </s>
            <s xml:id="echoid-s470" xml:space="preserve">Hujuſmodi plura exempla 2 propoſitionis exemplorum conſimi-
              <lb/>
            lia proponi poſſent, niſi jam ex antecedentibus innotuiſſent.</s>
            <s xml:id="echoid-s471" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div89" type="section" level="1" n="74">
          <head xml:id="echoid-head83" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s472" xml:space="preserve">B primi exempli, ſi poſſit fieri, 1 ℔ ponderoſius ſit, non erit gravioris pon-
              <lb/>
            deris ea ratio adlevius, quæ longioris radii eſt ad breviorem, quod 1 propoſi-
              <lb/>
            tioni repugnat. </s>
            <s xml:id="echoid-s473" xml:space="preserve">B igitur 1 ℔ ponderoſius non eſt. </s>
            <s xml:id="echoid-s474" xml:space="preserve">eodemq́ue pacto nequele-
              <lb/>
            vius eſſe demonſtrabitur. </s>
            <s xml:id="echoid-s475" xml:space="preserve">Ideoq́ue unam tantum ℔ pendebit, quod demon-
              <lb/>
            ſtrandum erat. </s>
            <s xml:id="echoid-s476" xml:space="preserve">*CONCLVSIO.</s>
            <s xml:id="echoid-s477" xml:space="preserve">* Datis igitur duobus ponderibus ſitu æ qui-
              <lb/>
            pondiis cognito ſcilicet, & </s>
            <s xml:id="echoid-s478" xml:space="preserve">incognito, datâ item anſâ. </s>
            <s xml:id="echoid-s479" xml:space="preserve">Incognitum pondus
              <lb/>
            cognitum fecimus, quod fuit quæſitum.</s>
            <s xml:id="echoid-s480" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div90" type="section" level="1" n="75">
          <head xml:id="echoid-head84" xml:space="preserve">3 PROBLEMA. 4 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s481" xml:space="preserve">Datis ponderibus cognitis ſitu æquipondiis, unàcum
              <lb/>
            lõgitudine radii alterius: </s>
            <s xml:id="echoid-s482" xml:space="preserve">reliqui radii lõgitudinĕ invenire.</s>
            <s xml:id="echoid-s483" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s484" xml:space="preserve">*DATVM.</s>
            <s xml:id="echoid-s485" xml:space="preserve">* A & </s>
            <s xml:id="echoid-s486" xml:space="preserve">B pondera ſitu æquipõdia ſunto, A quidem ex C ſuſpen-
              <lb/>
            ſum 3 ℔, B vero ex D 1 ℔ pendeat, & </s>
            <s xml:id="echoid-s487" xml:space="preserve">radius D E 6 pedes ſit longus.</s>
            <s xml:id="echoid-s488" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s489" xml:space="preserve">*QVAESITVM.</s>
            <s xml:id="echoid-s490" xml:space="preserve">* Reliqui radii longitudo nobis invenienda eſt.</s>
            <s xml:id="echoid-s491" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div91" type="section" level="1" n="76">
          <head xml:id="echoid-head85" xml:space="preserve">PRAGMATIA.</head>
          <p>
            <s xml:id="echoid-s492" xml:space="preserve">Proportio ſic erit, ut A 3 ℔ ad B 1 ℔. </s>
            <s xml:id="echoid-s493" xml:space="preserve">ita D E 6 pedes ad
              <lb/>
              <figure xlink:label="fig-527.01.018-01" xlink:href="fig-527.01.018-01a" number="25">
                <image file="527.01.018-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.018-01"/>
              </figure>
            E C 2. </s>
            <s xml:id="echoid-s494" xml:space="preserve">Plura exempla 2 propoſitionis exemplis conformia
              <lb/>
            hucadducere poſſemus, niſi ex antecedente doctrinâ ſatis no-
              <lb/>
            ta eſſent.</s>
            <s xml:id="echoid-s495" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div93" type="section" level="1" n="77">
          <head xml:id="echoid-head86" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s496" xml:space="preserve">Si E C duobus pedibus longior eſſe fingatur, longioris ra-
              <lb/>
            dii minor ratio fuerit ad breviorem, quam gravioris ponderis
              <lb/>
            ad levius, quod contra primam propoſitionem eſt. </s>
            <s xml:id="echoid-s497" xml:space="preserve">E C igi-
              <lb/>
            tur 2 pedibus nequaquam longior eſt. </s>
            <s xml:id="echoid-s498" xml:space="preserve">Similiter neq; </s>
            <s xml:id="echoid-s499" xml:space="preserve">brevior
              <lb/>
            eſſe demonſtrabitur, ut duos tantum pedes longum eſſe conſequens ſit, quod
              <lb/>
            erat demonſtrandum.</s>
            <s xml:id="echoid-s500" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s501" xml:space="preserve">*CONCLVSIO.</s>
            <s xml:id="echoid-s502" xml:space="preserve">* Datis igitur duobus ponderibus ſitu æquipondiis, & </s>
            <s xml:id="echoid-s503" xml:space="preserve">al-
              <lb/>
            terius radiorum longitudine: </s>
            <s xml:id="echoid-s504" xml:space="preserve">etiam reliqui longitudinem invenerimus, ut
              <lb/>
            petitum erat.</s>
            <s xml:id="echoid-s505" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div94" type="section" level="1" n="78">
          <head xml:id="echoid-head87" xml:space="preserve">4 PROBLEMA. 5 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s506" xml:space="preserve">Datâ columnâ pondus invenire, quod ad columnam
              <lb/>
            habeat datam rationem.</s>
            <s xml:id="echoid-s507" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s508" xml:space="preserve">*DATVM.</s>
            <s xml:id="echoid-s509" xml:space="preserve">* A B C D columna eſto, cujus axis E F, centrum G ſit, data au-
              <lb/>
            tem ratio 2 ad 3. </s>
            <s xml:id="echoid-s510" xml:space="preserve">*QVAESITVM.</s>
            <s xml:id="echoid-s511" xml:space="preserve">* Pondus ejus rationis erit ad datam co-
              <lb/>
            lumnam: </s>
            <s xml:id="echoid-s512" xml:space="preserve">quæ eſt 2 ad 3, hoc eſt columnæ {2/3}.</s>
            <s xml:id="echoid-s513" xml:space="preserve"/>
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